Fama-French Three-Factor Model Regression Estimator

CAPM says one factor explains returns. Fama and French showed size and value matter too. Set a portfolio's true factor exposures, generate a realistic return history, and watch how precisely, or imprecisely, regression actually recovers them.

How To Use This Model

Reading This Tool

Set a portfolio's true market, size (SMB), and value (HML) betas, plus true alpha.

The tool simulates 10 years of monthly factor and portfolio returns consistent with those true exposures, then runs OLS regression to estimate them back. Compare true versus estimated to see genuine sampling noise in action.

True Factor Exposures

True Monthly Alpha 0.20%

True Market Beta 1.15

True Size Beta (SMB) 0.35

True Value Beta (HML) -0.20

Idiosyncratic Noise (Monthly Std. Dev.) 1.0%

Simulation Seed 42

120 months (10 years) of factor and portfolio returns are simulated using this seed. Change the seed to see a fresh random sample drawn from the same true exposures.

True Vs. Estimated Betas

Market Beta: True → Estimated

SMB Beta: True → Estimated

HML Beta: True → Estimated

R-Squared

Fitted vs. Actual Simulated Portfolio Returns

Empirical Asset Pricing

The Core Regression

R_p − R_f = α + β_MKT(R_m−R_f) + β_SMB·SMB + β_HML·HML + ε

SMB (Small Minus Big) captures the historical excess return of small-cap over large-cap stocks. HML (High Minus Low) captures the excess return of high book-to-market (value) over low book-to-market (growth) stocks. Estimated via OLS multiple regression on monthly excess returns.

When To Actually Use This Model

Attributing a fund or portfolio's historical performance to systematic factor exposure versus genuine manager skill (alpha).
Teaching multi-factor asset pricing and the size and value anomalies in an empirical finance course.
Style analysis, confirming whether a "value fund" actually carries a positive HML loading as claimed.
Benchmarking manager alpha net of exposure to well-documented, low-cost-to-replicate risk factors.

Key Assumptions & Limitations

Assumes factor loadings are constant over the full estimation window; in practice they drift and are often estimated on rolling windows.
Three factors leave meaningful return variation unexplained for many portfolios, motivating extensions like the Fama-French five-factor model (adding profitability and investment).
Statistical significance of individual coefficients depends on standard errors not shown in this simplified point-estimate tool.
Simulated data here uses independent normal factors; real factors are correlated and not normally distributed.

Foundational Reference

Fama, E. F., & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1), 3-56.

Want the single-factor CAPM comparison?

Open The CAPM Tool →